Hi, A common use case for 'on' (from Data.Function) is to use it with 'compare', e.g. 'compare `on` snd'. In fact, this pattern is so common that there's a convenient 'comparing' function which provides a shortcut for this use case such that one can write sortBy (comparing snd) instead of sortBy (compare `on` snd) I think another common use case is to use 'on' together with (==) as in groupBy ((==) `on` snd) In a similiar vein as with 'comparing', I think it would be nice if there was a function which encapsulates this use case, like equating :: Eq b => (a -> b) -> a -> a -> Bool equating = on (==) such that one can write groupBy (equating snd) In fact, groupBy is just one of many *By functions taking an a -> a -> Bool -- many of which are Data.List, e.g. groupBy, nubBy, deleteBy, intersectBy, unionBy. Hence, it seems plausible to define 'equating' in Data.List. This is the same reasoning as why 'comparing' is in Data.Ord: because the module exposes a lot of *By functions taking an a -> a -> Ordering. - Frerich